Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables (the current density and the superconducting order parameter, respectively) are included in the density-functional formalism. Here we show that the corresponding conjugate potentials (vector and pair potentials, respectively) are { \it not} uniquely determined by the densities. The Hohenberg-Kohn theorem of these generalized density-functional theories is thus weaker than the original one. We give explicit examples and explore some consequences.
Categories: cond-mat.mtrl-sci cond-mat.str-el cond-mat.supr-con